Crystal Palace may not yet have a manager, but they still have hope. Their first clean sheet of the season brought reward for a resolute performance that frustrated humdrum Everton and suggested the south London side may not, after all, be doomed to relegation. At least not by a record margin.

A seven-match losing streak had spawned fears that Derby County's all-time-low Premier League tally of 11 points in the 2007-08 season may not be beyond Palace but this display testified to the club's determination to defy such forebodings. Palace were well-drilled and diligent; Everton were disappointingly devoid of inspiration.

Palace have admitted they were ill-prepared for their promotion to the top flight and a haul of four points from their first 11 games stands as cruel confirmation. The club are attempting to rebuild on the fly and the first stone was put in place before kick-off, when a sporting director was appointed. Iain Moody, who was ousted from Cardiff City last month on a whim of that club's owner, Vincent Tan, will handle player recruitment as Palace attempt to embed a playing philosophy that will deliver long-term continuity.

A more immediate matter is the hiring of a manager and the club expects to do that later this week, with José Mourinho's former assistant at Real Madrid, Aitor Karanka, among the candidates scheduled to hold further talks with Palace's co-chairman Steve Parish. The visit of Everton, then, is likely to be Keith Millen's last match at the helm. If it is, he went out on a high.

Millen's previous two matches since succeeding Ian Holloway ended in defeat, but the performances were encouraging enough for him to make just one change to the lineup that lost at West Bromwich Albion, with Yannick Bolasie replacing the injured Adlène Guédioura. The team delivered a display that, with better finishing, would have yielded a victory.

Leon Osman skewed two early shots wide for Everton and Kevin Mirallas registered the first effort on target in the 20th minute, when his drive from the edge of the area was pushed behind by Julian Speroni. Everton's possession was mostly sterile as Palace, for whom Danny Gabbidon and Damien Delaney were outstanding, kept them at bay.

Palace's counterattacks started to alarm Everton. The hosts should have taken the lead in the 35th minute, when Kagisho Dikgacoi surged on to Jerome Thomas's cross but got himself in a muddle at the back post and failed to even fire a shot. Moments later, Thomas unleashed a curling shot from 20 yards out that sent Tim Howard leaping to his left to tip the ball wide. Marouane Chamakh headed Barry Bannan's cross wide from six yards out.

Everton regained control in the second half but still lacked invention and, in the 54th minute, Palace created the best chance of the match, Bolasie spinning away from Leighton Baines before sending Thomas racing free on goal. As the long-suffering Selhurst Park crowd rose to their feet in anticipation, Thomas chipped the ball over Howard, but wide.

Palace then had to withstand fierce Everton pressure in the dying minutes but although Phil Jagielka sent a late header against their crossbar, the visitors were not creative enough to earn three points. "If this was my last game, I walk out with a smile on my face," Millen said. "I think I've left a squad of players that want to fight for this club. I believe there is enough quality in this squad to compete with five or six of the lower teams."